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The multiple job class scheduling problem arises in contexts where a group of jobs belong to multiple classes and in which if all jobs in the same class are operated together, extra setup times would not be needed. On the other hand, the customer order scheduling problem focuses on finishing all jobs from the same order at the same time in order to reduce shipping costs. However, works on customer orders coupled with class setup times do not appear often in the literature. Hence we address here a bicriteria single machine customer order scheduling problem together with multiple job classes. The optimality criterion minimizes a linear combination of the sum of the ranges and sum of tardiness of all customer orders. In light of the high complexity of the concerned problem, we propose a lower bound formula and a property to be used in a branch-and-bound method for optimal solutions. To find approximate solutions, we then propose four heuristics together with a local search method, four cloudy theoretical simulated annealing and a cloudy theoretical simulated annealing hyperheuristic along with five low-level heuristics. The simulation results of the proposed heuristics and algorithms are analyzed.

The customer’s order (CO) issues have received growing attention in the scheduling research community. In the CO design, a customer’s order consists of several components, and the processed orders are assigned to m parallel machines. The completion time of an order is assumed at the time at which all components in a customer’s order are finished. In the published articles, the processing times of all components were considered as fixed and known numbers in customer order scheduling problems. This assumption is indeed at odds in many real practical productions in which there exist a lot of relevant uncertainty factors; for example, machine may break down, the working situation may change, some operator’s performance may become instability, and so on. In such a situation, the processing times of given jobs are impropriate assumed as fixed and constant numbers. Thus, this article introduces a customer’s order scheduling problem on m parallel machines along with scenario-dependent processing times of all components and scenario-dependent due dates. Based on the worse case, the measurement rule is to find an appropriate policy to minimize the maximum total tardiness of given n customer’s orders across the possible scenarios among all possible schedules. In this study we derive several dominant rules and lower bounds used in a branch-and-bound method searching for exact solutions. Subsequently, we propose several heuristics and an iterated greedy algorithm with and without a population-based for finding approximate solutions. Finally, the computational results of all proposed algorithms are tested and reported.

Recently, the setup times or costs have become an important research topic. The main reason is huge economic savings can be achieved when setup times are explicitly included in scheduling decisions in various real-world industrial environments. On the other hand, many real systems commonly face various uncertainties, such as working environment changes, machine breakages, a worker becomes unstable, etc. In such an environment, job-processing times should not be fixed numbers. Motivated by these situations, this article introduces a single-machine scheduling problem with sequence-dependent setup times and scenario-dependent processing times where the objective function is the total completion time. The robust version of this problem without setup times has been shown to be NP hard. To tackle this problem, a lower bound and a dominance rule are derived in a branch-and-bound method for finding an optimal solution. As for determining approximate solutions, five neighborhood schemes are proposed and embedded in the cloud theory-based simulated annealing. Finally, the performances of all proposed algorithms are determined and compared.

Recently, finding solutions to assembly flowshop scheduling problems is a topic of extensive discussion in research communities. While existing research assumes that job processing times are consta...

Scheduling with multiple agents and learning effects has attracted growing attention of the scheduling research community. However, scheduling research together with learning, multiple agents and r...

This article addresses a two-stage, three-machine assembly scheduling problem that considers the learning effect. All jobs are processed on two machines in the first stage and move on to be process...

This paper studies the slack due-window assignment method for single-machine scheduling problems with position-and resource-dependent processing times, for which the actual processing time is a con...

This study examines a two-stage three-machine flow-shop assembly scheduling model in which job processing time is considered as a mixed function of a controlled truncation parameter with a sum-of-processing-times-based learning effect. However, the truncation function is very limited in the two-stage flow-shop assembly scheduling settings. To overcome this limitation, this study investigates a two-stage three-machine flow-shop assembly problem with a truncation learning function where the makespan criterion (completion of the last job) is minimized. Given that the proposed model is NP hard, dominance rules, lemmas and a lower bound are derived and applied to the branch-and-bound method. A dynamic differential evolution algorithm, a hybrid greedy iterated algorithm and a genetic algorithm are also proposed for searching approximate solutions. Results obtained from test experiments validate the performance of all the proposed algorithms.

This paper introduces a two-stage assembly flowshop scheduling model with time cumulated learning effect, which exists in many realistic scheduling settings. By the time cumulated learning effect, we mean that the actual job processing time of a job depends on its scheduled position as well as the processing times of the jobs already processed. The first stage consists of two independently working machines where each machine produces its own component. The second stage consists of a single assembly machine. The objective is to identify a schedule that minimizes the total completion time of all jobs. With analysis on the discussed problem, some dominance rules are developed to optimize the solving procedure. Incorporating with the developed dominance rules, a dominance rule and opposition-based particle swarm optimization algorithm (DR-OPSO) and branch-and-bound are devised. Computational experiments have been conducted to compare the performances of the proposed DR-OPSO and branch-and-bound through comparing with the standard O-PSO and PSO. The results fully demonstrate the efficiency and effectiveness of the proposed DR-OPSO algorithm, providing references to the relevant decision-makers in practice.

The two-stage assembly scheduling problem has attracted increasing research attention. In many such problems, job processing times are commonly assumed to be fixed. However, this assumption does not hold in many real production situations. In fact, processing times usually decrease steadily when the same task is performed repeatedly. Therefore, in this study, we investigated a two-stage assembly position-based learning scheduling problem with two machines in the first stage and an assembly machine in the second stage. The objective was to complete all jobs as soon as possible (or to minimise the makespan, implying that the system can perform better and efficient task planning with limited resources). Because this problem is NP-hard, we derived some dominance relations and a lower bound for the branch-and-bound method for finding the optimal solution. We also propose three heuristics, three versions of the simulated annealing (SA) algorithm, and three versions of cloud theory-based simulated annealing algo...

We study a two-agent multi-facility order scheduling with ready times.We derive several dominance properties and a lower bound on the optimal solution.We present algorithms based on particle swarm optimization (PSO) and opposite-based particle swarm optimization (O-PSO) to obtain near-optimal solutions. Recently, multi-agent scheduling and customer order scheduling have separately received much attention in scheduling research. However, the two-agent concept has not been introduced into order scheduling in the multi-facility setting. To fill this research gap, we consider in this paper two-agent multi-facility order scheduling with ready times. The objective is to minimize the total completion time of the orders of one agent, with the restriction that the total completion time of the orders of the other agent cannot exceed a given limit. We first develop a branch-and-bound algorithm incorporating several dominance rules and a lower bound to solve this intractable problem. We then propose a particle swarm optimization algorithm (PSO), an opposite-based particle swarm optimization (OPSO) algorithm, and a particle swarm optimization algorithm with a linearly decreasing inertia weight (WPSO) to obtain near-optimal solutions. Applying two levels of number of particles and number of neighbourhood improvements for the PSO and OPSO algorithms, we execute them at a fixed inertia weight, and execute WPSO at a varying decreasing inertia weight. We perform a one-way analysis of variance of the performance of the five PSO algorithms in tackling the problem with small and big orders. We demonstrate through extensive computational studies that the proposed PSO algorithms are very efficient in quickly finding solutions that are very close to the optimal solutions.

Many practical productions are full of significant uncertainties. For example, the working environment may change, machines may breakdown, workers may become unstable, etc. In such an environment, job processing times should not be fixed numbers. In light of this situation, we investigate a single-machine problem with two-scenario-based processing times, where the goal is to minimize the maximum total completion times over two scenarios. When the uncertainty of the job processing times is confronted, the robust version of this problem is NP-hard, even for very restricted cases. To solve this problem, we derive some dominance rules and a lower bound for developing branch-and-bound algorithms to find optimal solutions. As for determining approximate solutions, we propose five heuristics, adopting combined two-scenario-based dependent processing times, to produce initial solutions and then improve each with a pairwise interchange. Further, we propose a simulated annealing hyper-heuristic incorporating the proposed seven low level heuristics to solve this problem as well. Finally, the performances of all proposed algorithms are tested and reported.

This paper considers two-agent just-in-time scheduling where agents A and B have to share m unrelated parallel machines for processing their jobs. The objective of agent A is to maximize the weighted number of its just-in-time jobs that are completed exactly on their due dates, while the objective of agent B is either to maximize its maximum gain (income) from its just-in-time jobs or to maximize the weighted number of its just-in-time jobs. We provide a bicriterion analysis of the problem, which seek to find the Pareto-optimal solutions for each combination of the two agents׳ criteria. When the number of machines is part of the problem instance, both the addressed problems are NP-hard in the strong sense. When the number of machines is fixed, we show that the problem of maximizing agent A׳s weighted number of just-in-time jobs while maximizing agent B׳s maximum gain can be solved in polynomial time, whereas the problem of maximizing both agents׳ weighted numbers of just-in-time jobs is NP-hard. For the latter problem, we also provide a pseudo-polynomial-time solution algorithm, establishing that it is NP-hard in the ordinary sense, and show that it admits a fully polynomial-time approximation scheme (FPTAS) for finding an approximate Pareto solution.

In many resource allocation problems in physical or economic systems, a linear resource consumption function is commonly considered, and job processing times are assumed to be fixed parameters. However, the former assumption fails to reflect the law of diminishing returns, and the latter may be controlled by changing the allocation of resources to jobs. Motivated by these observations, we provide a unified model for solving single-machine scheduling problems in which each job's processing time is a function of its starting time and convex resource allocation. The objective is to find the optimal sequence of jobs subject to a limited resource consumption. We first show how this unified model can be useful in solving scheduling problems under due date assignment considerations. We analyze the problem with four different due date assignment methods, and our objective function includes costs for earliness, tardiness and due date assignments. We also consider scheduling problems without involving due date assignment decisions. The objective function is to minimize the makespan, total completion time, total absolute variation in completion times, and total absolute variation in waiting times. We show that several existing well-known problems can be reduced to a special case of our unified model and solved in O ( n log n ) time.

Manufacturing industry reflects a country&rsquo, s productivity level and occupies an important share in the national economy of developed countries in the world. Jobshop scheduling (JSS) model originates from modern manufacturing, in which a number of tasks are executed individually on a series of processors following their preset processing routes. This study addresses a JSS problem with the criterion of minimizing total quadratic completion time (TQCT), where each task is available at its own release date. Constructive heuristic and meta-heuristic algorithms are introduced to handle different scale instances as the problem is NP-hard. Given that the shortest-processing-time (SPT)-based heuristic and dense scheduling rule are effective for the TQCT criterion and the JSS problem, respectively, an innovative heuristic combining SPT and dense scheduling rule is put forward to provide feasible solutions for large-scale instances. A preemptive single-machine-based lower bound is designed to estimate the optimal schedule and reveal the performance of the heuristic. Differential evolution algorithm is a global search algorithm on the basis of population, which has the advantages of simple structure, strong robustness, fast convergence, and easy implementation. Therefore, a hybrid discrete differential evolution (HDDE) algorithm is presented to obtain near-optimal solutions for medium-scale instances, where multi-point insertion and a local search scheme enhance the quality of final solutions. The superiority of the HDDE algorithm is highlighted by contrast experiments with population-based meta-heuristics, i.e., ant colony optimization (ACO), particle swarm optimization (PSO) and genetic algorithm (GA). Average gaps 45.62, 63.38 and 188.46 between HDDE with ACO, PSO and GA, respectively, are demonstrated by the numerical results with benchmark data, which reveals the domination of the proposed HDDE algorithm.

Job precedence can be found in some real-life situations. For the application in the scheduling of patients from multiple waiting lines or different physicians, patients in the same waiting line for scarce resources such as organs, or with the same physician often need to be treated on the first-come, first-served basis to avoid ethical or legal issues, and precedence constraints can restrict their treatment sequence. In view of this observation, this paper considers a two-machine flowshop scheduling problem with precedence constraint on two jobs with the goal to find a sequence that minimizes the total tardiness criterion. In searching solutions to this problem, we build a branch-and-bound method incorporating several dominances and a lower bound to find an optimal solution. In addition, we also develop a genetic and larger-order-value method to find a near-optimal solution. Finally, we conduct the computational experiments to evaluate the performances of all the proposed algorithms.

This paper addresses some scheduling problems with two competing agents, called agents A and B, respectively, each of which has a set of independent nonpreemptive jobs to be scheduled for processing on a common machine. The due dates of jobs in each job set are considered as given parameters and must be assigned to individual jobs. Each agent wants to minimize a certain objective function that depends on the completion times and due dates of its jobs only. The goal is to find a feasible schedule and determine the due dates for all jobs of the two agents that minimizes the objective of agent A while keeping the objective of agent B below or at a fixed level Q. We consider nine problems arising from different criteria combinations for the two agents, depending on the criterion of each agent including the maximum lateness, total (weighted) tardiness, (weighted) number of tardy jobs, and total weighted tardiness and earliness, and state the complexity results for most of problems under consideration.

We study a single-machine due date assignment and scheduling problem involving two agents each seeking to optimise its own performance. We consider three due date assignment methods, namely the common, slack and unrestricted due date assignment methods. For each due date assignment method, we consider two types of optimisation problem, namely a linear combination optimisation problem (minimising the total integrated cost of the two agents) and a constrained optimisation problem (minimising the objective of one agent, subject to an upper bound on the objective of the other agent). We present a polynomial-time dynamic programming algorithm to solve the linear combination optimisation problem, and show that the constrained optimisation problem is -hard in the ordinary sense and admits a fully polynomial-time approximation scheme.

Purpose – The primary purpose of this paper is to integrate unified theory of acceptance and use of technology (UTAUT) and website service quality, compiling it into a usage behavioural model for university library electronic resources. Design/methodology/approach – Using structural equation model technology to verify model fit. Questionnaire surveys are the main research methodology in this study, in which fourth-year university students and second-year Master’s students in six Taiwan public and private universities are the research population. This study uses a cluster sampling, releasing 1,206 questionnaires, and retrieves 1,089 valid questionnaires, for a valid retrieval rate of 90.3 per cent. Findings – The conclusions are: this study has good fit in the model, and is applicable for the UTAUT; the pairs of variables are correlated; public or private and school type have partial significant mediating effect; website service quality has a significant positive influence on behavioural intention; performance expectancy and social influence both positively affect behavioural intention; facilitating conditions positively affect use behaviour. Originality/value – Empirical research results and suggestions are provided for the relevant departments for practice and future academic research.

Scheduling with learning effects has received a lot of research attention lately. On the other hand, it is commonly seen that time restrictions are usually modeled by due dates or deadlines and the quality of schedules is estimated with reference to these parameters. One of the performance measures involving due dates is the late work criterion, which is relatively unexplored. Thus, we study a single-machine scheduling problem with a position-based learning effect. The objective is to minimize the total late work, where the late work for a job is the amount of processing of this job that is performed after its due date. We attempt to develop a branch-and-bound algorithm incorporating with some dominance rules and a lower bound for the optimal solution. For saving computational time, we also propose three heuristic-based genetic algorithms for the near-optimal solution. Finally, the computational results of proposed algorithms are also provided.

In this paper, we explore a single-machine scheduling problem in which the processing time of a job is a linear increasing function of its starting time. The objective is to determine the optimal due date and schedule simultaneously to minimize a cost function that includes the weighted number of tardy jobs and the due date assignment cost. We show that the problem is NP-hard in the ordinary sense. In addition, we propose two dynamic programming algorithms and a fully polynomial-time approximation scheme for the problem.

We consider several two-agent scheduling problems, where agents A and B have to share a single machine while processing their jobs. The objective is to minimize a certain objective function which depends on the completion time of all the jobs, while keeping the objective of agent B (with regard to its jobs only) below or at a fixed level Q. Specifically, we focus on minimizing certain objective functions of all the jobs such as maximum earliness cost, total weighted earliness cost, and total weighted earliness and tardiness cost, subject to an upper bound on a certain objective function of agent B. We introduce polynomial time solution for the maximum earliness cost problem, and prove NP-hardness for the total weighted earliness cost and total weighted earliness and tardiness cost cases. We also discuss some polynomially solvable cases for the total weighted earliness cost problem.

We consider batch delivery scheduling on a single machine, where a common due-date is assigned to all the jobs and a rate-modifying activity on the machine may be scheduled, which can change the processing rate of the machine. Thus the actual processing time of a job is variable depending on whether it is processed before or after the rate-modifying activity. The objective is to determine the optimal job sequence, the optimal partition of the job sequence into batches, the optimal assigned common due-date, and the optimal location of the rate-modifying activity simultaneously to minimize the total cost of earliness, job holding, weighted number of tardy jobs, due-date assignment, and batch delivery. We derive some structural properties of the problem, based on which we design polynomial-time algorithms to solve some special cases of the problem.

Recently, both the learning effect scheduling and re-entrant scheduling have received more attention separately in research community. However, the learning effect concept has not been introduced into re-entrant scheduling in the environment setting. To fill this research gap, we investigate re-entrant permutation flowshop scheduling with a position-based learning effect to minimize the total completion time. Because the same problem without learning or re-entrant has been proved NP-hard, we thus develop some heuristics and a genetic algorithm (GA) to search for approximate solutions. To solve this problem, we first adopt four existed heuristics for the problem; we then apply the same four methods combined with three local searches to solve the proposed problem; in the last stage we develop a heuristic-based genetic algorithm seeded with four good different initials obtained from the second stage for finding a good quality of solutions. Finally, we conduct experimental tests to evaluate the behaviours of all the proposed algorithms when the number of re-entrant times or machine number or learning effect or job size changes.

This paper considers single-machine scheduling problems with simultaneous consideration of due date assignment, past-sequence-dependent (p-s-d) delivery times, and position-dependent learning effects. By p-s-d delivery times, we mean that the delivery time of a job is proportional to the job’s waiting time. Specifically, we study four variants of the problem: (i) the variant of total earliness and tardiness with common due date assignment (referred to as TETDC), (ii) the variant of total earliness and weighted number of tardy jobs with CON due date assignment (referred to as TEWNTDC), (iii) the variant of total earliness and weighted number of tardy jobs with slack due date assignment (referred to as TEWNTDS), and (iv) the variant of weighted number of tardy jobs with different due date assignment (referred to as WNTDD). We derive the structural properties of the optimal schedules and show that the variants TETDC, TEWNTDC and TEWNTDS are all polynomially solvable. Although the complexity status of the variant WNTDD is still open, we show that two special cases of it are polynomially solvable.

In this paper we consider the problem of single-machine batch delivery scheduling with an assignable common due date and controllable processing times. The job processing time is either a linear or a convex function of the amount of a continuously divisible and non-renewable resource allocated to the job. Finished jobs are delivered in batches and there is no capacity limit on each delivery batch. The objective is to find a job sequence, a partition of the job sequence into batches, a common due date, and resource allocation that jointly minimise a cost function based on earliness, weighted number of tardy jobs, job holding, due-date assignment, batch delivery, makespan, and resource consumption. We provide some properties of the optimal solution, and show that the problem with the linear and convex resource consumption functions can be solved in and time, respectively. We also show that some special cases of the problem can be solved by lower-order algorithms.

Honey was a particular matrix with a variety of composition and origin, which lead to different degree of matrix effect on analytes. As a rule, the matrix-matched calibration curve from blank honey was adopted to quantifying analyte in a batch. This paper investigated matrix effect on sulfonamide in four honey samples by high-performance liquid chromatography hyphenated with mass spectrometry detection. The main goal was to check whether matrix-matched calibration curve obtained from a random blank honey could match the real samples in character within current recommended acceptance criteria. It was found that analyte recovery from true matrix-matched standard calibration curve ranged 87.7-117.3%, whereas recovery from surrogate matrix-matched calibration curves gave a very wide range from 54.3 to 150.2%, far beyond the acceptance criteria. So it was perhaps not feasible to use a surrogated blank sample to prepare matrix-matched calibration curve for quantifying analyte, particularly for largely diverse honey samples in a batch. To reduce error from inter-sample matrix effect, the best solution seemed to use internal standard or standard addition.

We consider single-machine batch delivery scheduling with an assignable common due date and controllable processing times, which vary as a convex function of the amounts of a continuously divisible common resource allocated to individual jobs. Finished jobs are delivered in batches and there is no capacity limit on each delivery batch. We first provide an O(n^5) dynamic programming algorithm to find the optimal job sequence, the partition of the job sequence into batches, the assigned common due date, and the resource allocation that minimize a cost function based on earliness, tardiness, job holding, due date assignment, batch delivery, and resource consumption. We show that a special case of the problem can be solved by a lower-order polynomial algorithm. We then study the problem of finding the optimal solution to minimize the total cost of earliness, tardiness, job holding, and due date assignment, subject to limited resource availability, and develop an O(nlogn) algorithm to solve it.

Scheduling with learning effects has received growing attention nowadays. A well-known learning model is called ‘position-based learning’ in which the actual processing time of a job is a non-increasing function of its position to be processed. However, the actual processing time of a given job drops to zero precipitously as the number of jobs increases. Motivated by this observation, we propose two truncated learning models in single-machine scheduling problems and two-machine flowshop scheduling problems with ordered job processing times, respectively, where the actual processing time of a job is a function of its position and a control parameter. Under the proposed learning models, we show that some scheduling problems can be solved in polynomial time. In addition, we further analyse the worst-case error bounds for the problems to minimize the total weighted completion time, discounted total weighted completion time and maximum lateness.

In many real-life scheduling environments, the jobs deteriorate at a certain rate while waiting to be processed. This paper addresses some single-machine scheduling problems with past-sequence-dependent (p-s-d) delivery times and a linear deterioration. The p-s-d delivery time of a job is proportional to the job's waiting time. It is assumed that the deterioration process is reflected in the job processing times being an increasing function of their starting times. We consider the following objectives: the makespan, total completion time, total weighted completion time, maximum lateness, and total absolute differences in completion times. We seek the optimal schedules for the problems to minimize the makespan and total completion time. Despite that the computational complexities of the problems to minimize the total weighted completion time and maximum lateness remain open, we present heuristics and analyze their worst-case performance ratios, and show that some special cases of the problems are polynomially solvable. We also show that the optimal schedule for the problem to minimize the total absolute differences in completion times is $V$-shaped with respect to the normal job processing times.

Scheduling with learning effects has continued to attract the attention of scheduling researchers. However, the majority of the research on this topic has been focused on the single-machine setting. Moreover, under the commonly adopted learning model in scheduling, the actual processing time of a job drops to zero precipitously as the number of jobs increases, which is at odds with reality. To address these issues, we study a two-machine flowshop scheduling problem with a truncated learning function in which the actual processing time of a job is a function of the job's position in a schedule and the learning truncation parameter. The objective is to minimize the makespan. We propose a branch-and-bound and three crossover-based genetic algorithms (GAs) to find the optimal and approximate solutions, respectively, for the problem. We perform extensive computational experiments to evaluate the performance of all the proposed algorithms under different experimental conditions. The results show that the GAs perform quite well in terms of both efficiency and solution quality.

This paper addresses a two-agent scheduling problem on a single machine with arbitrary release dates, where the objective is to minimize the tardiness of one agent, while keeping the lateness of the other agent below or at a fixed level Q. A mixed integer programming model is first presented for its optimal solution, admittedly not to be practical or useful in the most cases, but theoretically interesting since it models the problem. Thus, as an alternative, a branch-and-bound algorithm incorporating with several dominance properties and a lower bound is provided to derive the optimal solution and a marriage in honey-bees optimization algorithm (MBO) is developed to derive the near-optimal solutions for the problem. Computational results are also presented to evaluate the performance of the proposed algorithms.

We consider several two-agent scheduling problems with assignable due dates on a single machine, where each of the agents wants to minimize a measure depending on the completion times of its own jobs and the due dates are treated as given variables and must be assigned to individual jobs. The goal is to assign a due date from a given set of due dates and a position in the sequence to each job so that the weighted sum of the objectives of both agents is minimized. For different combinations of the objectives, which include the maximum lateness, total (weighted) tardiness, and total (weighted) number of tardy jobs, we provide the complexity results and solve the corresponding problems, if possible.

This article introduces a general single-machine setup times scheduling model with learning effect and deteriorating jobs simultaneously which is a generalisation of some existing models in the literature. The setup times are proportional to the length of the already processed jobs, i.e. the setup times are past-sequence-dependent p-s-d. By the effects of learning and deterioration, we mean that the actual processing time of a job depends not only on the starting time of the job but also on its scheduled position. The article shows that the problems to minimise the makespan, sum of the k th power of completion times, total lateness and sum of earliness penalties with common due date are polynomially solvable under the proposed model. It further shows that the problems to minimise total weighted completion time, maximum lateness, maximum tardiness, total tardiness and total weighted earliness penalties with common due date are polynomially solvable under certain conditions.

This study addresses the problem of minimizing the total weighted tardiness on a single-machine with a position-based learning effect. Several dominance properties are established to develop branch and bound algorithm and a lower bound is provided to derive the optimal solution. In addition, three heuristic procedures are developed for near-optimal solutions. Computational results are also presented to evaluate the performance of the proposed algorithms.

We consider a scheduling environment with two agents and a linear non-increasing deterioration. By the linear non-increasing deterioration we mean that the actual processing time of a job belonging to the two agents is defined as a non-increasing linear function of its starting time. Two agents compete to perform their respective jobs on a common single machine and each agent has his own criterion to be optimized. The goal is to schedule the jobs such that the combined schedule performs well with respect to the measures of both agents. Three different objective functions are considered for one agent, including the maximum earliness cost, total earliness cost and total weighted earliness cost, while keeping the maximum earliness cost of the other agent below or at a fixed level U. We propose the optimal (nondominated) properties and present the complexity results for the problems addressed here.

Honey has always been the center of focus, not only because of its valuable nutrition, but also because of its use as an environmental indicator. In this context, 10 honey samples from Taiwan and Mainland China were collected to detect concentration of 17 PCDD/Fs, 12 dioxin-like PCBs and 27 metal elements by HRCG/HRMS and ICP-MS. The main goal was to investigate the difference between honeys of diverse geographical origins and to validate the feasibility of honey being an environmental bioindicator. The result showed lower concentration of PCDD/Fs and dioxin-like PCBs than their MDLs, indicating it was not feasible using honey as the indicator for these compounds in the environment. The result for metal elements showed a higher concentration of K, Na, Mg and Ca in honey from Taiwan than those from the Mainland. Toxic element, As, Ba, Pb, Cd, Cr, Ag, were all found present in honey from the Mainland; while only three of those, Ba, Pb, Cd were detectible in honey from Taiwan. This could imply a much more complex pollution source in the Mainland than in Taiwan

Scheduling with deteriorating jobs and learning effects has been widely studied. However, multi-agent scheduling with simultaneous considerations of deteriorating jobs and learning effects has hardly been considered until now. In view of this, we consider a two-agent single-machine scheduling problem involving deteriorating jobs and learning effects simultaneously. In the proposed model, given a schedule, we assume that the actual processing time of a job of the first agent is a function of position-based learning while the actual processing time of a job of the second agent is a function of position-based deterioration. The objective is to minimize the total weighted completion time of the jobs of the first agent with the restriction that no tardy job is allowed for the second agent. We develop a branch-and-bound and several simulated annealing algorithms to solve the problem. Computational results show that the proposed algorithms are efficient in producing near-optimal solutions.